This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...
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1answer
44 views
Small World Problem [closed]
Im sure many of you have heard of the small world problem. I've tried to model it using the following set up and I was wondering if there's any interesting questions to come out of it. Suppose we have ...
2
votes
1answer
25 views
What is the difference between a probability distribution on events and random variables?
For the purpose of simplicity, assume everything below is only in the discrete domain.
A $\text{probability space}$ is usually defined as a triple $(\Omega , 2^\Omega , P)$ where
$\Omega := ...
0
votes
1answer
20 views
Optimize winnings in a money making game.
So, given a continuous random variable A (with some density and CDF function), and a value I choose V, what is the equation to determine the best value V to maximize my earnings given that I will be ...
3
votes
0answers
14 views
2-dimensional percolation and a random graph
Imagine turning the square grid defined by $\mathbb{N}^2$ in the plane into a directed graph. The vertices are $\mathbb{N}^2$ and for each vertex $(x,y)$, there is an edge pointing from it to $(x+1, ...
2
votes
1answer
32 views
How gaussian mixture models work?
I am given an example:
Suppose 1000 observations are drawn from $N(0,1)$ and $N(5,2)$ with mixing parameters $\pi_{1}=0.2$ and $\pi_{2}=0.8$ respectively. Suppose we only know $\sigma$ and want to ...
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votes
0answers
18 views
How do you calculate total impact from a number of correlated events
Say that you have 10 events that each have a probability from 0% to 100% and each have a potential impact that is either 0 if the event doesn't happen or a number between $0-$10 if the event does ...
4
votes
2answers
54 views
A classical problem in combinatorics/probability
I read this problem in Cognition and Chance by Raymond Nickerson (the problem is stated not discussed)
...
-2
votes
2answers
44 views
expected value and variance of getting a head or a tail right after each other when flipping a fair coin
[this is a classic problem appeared on a mathematical journal. i see someone already asked it here but i still don't get it. i think it's interesting to get through it with some thoughtful ideas]
we ...
3
votes
1answer
36 views
30-sided die, 2-player game
Two players play a game. Player 1 goes first, and chooses a number between 1 and 30 (inclusive). Player 2 chooses second; he can't choose Player 1's number. A fair 30-sided die is rolled. The player ...
2
votes
1answer
28 views
Sum of stationary process
Suppose you have two stationary process $A_{t}$ and $B_{t}$. Suppose $Z_{t} = A_{t} + B_{t}$. Show that $Z_{t}$ is stationary. I am unsure how to solve this without knowing if the processes are ...
0
votes
1answer
25 views
Product of stationary stochastic process
Suppose $z_{t} = x_{t}y_{t}$ where $x_{t}$ and $y_{t}$ are 0 mean, independent stationary stochastic process. What is the autocovariance function of $z_{t}$? Show that the spectral density can be ...
2
votes
3answers
47 views
Lebesgue measure on $\mathbb{R}$ is not a probability measure
So I'm not a math student hence the (probably rather simple) question in the title. I could not find an answer in the slides or the internet.
My intuition is that the elements (ie. reals) of ...
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vote
2answers
34 views
Probability of winning a game
$A$ and $B$ play a game.
The probability of $A$ winning is $0.55$.
The probability of $B$ winning is $0.35$.
The probability of a tie is $0.10$.
The winner of the game is ...
0
votes
1answer
10 views
How to count permutations with restrictions on how items are grouped
I am trying to solve the following problem:
A town contains $4$ people who repair televisions. If $4$ sets break down, what is the probability that exactly $i$ of the repairers are called? Solve ...
0
votes
2answers
22 views
densities being absolutely continuous wrt Lebesgue measure
I'm reading an article with an assumption similar to: "The density $f(.)$ exists and is absolutely continuous with respect to Lebesgue measure". I don't understand this assumption because $f$ is not ...
